Advertisement

Time Reversal and Imaging for Structures

  • C. G. Panagiotopoulos
  • Y. Petromichelakis
  • C. Tsogka
Chapter
Part of the Lecture Notes in Civil Engineering book series (LNCE, volume 2)

Abstract

We present a numerical implementation of the time-reversal (TR) process in the framework of structural health monitoring. In this setting, TR can be used for localizing shocks on structures, as well as, for detecting and localizing defects and areas which have suffered damage. In particular, the present study is focused on beam assemblies, typically utilized for simulating structures of civil engineering interest. For that purpose, Timoshenko’s beam theory is employed since it is more adequate for describing higher-frequency phenomena. The numerical procedure is explained in detail and the capabilities of the proposed methodology are illustrated with several numerical results.

Keywords

Time-reversal Structural health monitoring Finite element method Imaging 

Notes

Acknowledgements

This work was partially supported by the European Research Council Starting Grant Project ADAPTIVES-239959.

References

  1. Ammari H, Bretin E, Garnier J, Wahab A (2013) Time-reversal algorithms in viscoelastic media. Eur J Appl Math 24(04):565–600MathSciNetCrossRefzbMATHGoogle Scholar
  2. Anderson BE, Griffa M, Larmat C, Ulrich TJ, Johnson PA (2008) Time reversal. Acoust Today 4(1):5–16CrossRefGoogle Scholar
  3. Bathe K-J (2006) Finite element procedures. Klaus-Jurgen BatheGoogle Scholar
  4. Bécache E, Joly P, Tsogka C (2002) A new family of mixed finite elements for the linear elastodynamic problem. SIAM J Numer Anal 39:2109–2132MathSciNetCrossRefzbMATHGoogle Scholar
  5. Belytschko T, Hughes TJ (2014) Computational methods for transient analysis. Comput Methods Mech 1Google Scholar
  6. Bleistein N, Cohen J, John W (2001) Mathematics of multidimensional seismic imaging, migration, and inversion. Springer Science+Business Media, New YorkCrossRefzbMATHGoogle Scholar
  7. Borcea L, Papanicolaou G, Tsogka C (2005) Interferometric array imaging in clutter. Inverse Probl 21(4):1419MathSciNetCrossRefzbMATHGoogle Scholar
  8. Clough RW, Penzien J (1993) Dynamics of structures. McGraw-Hill, SingaporezbMATHGoogle Scholar
  9. Cook RD, Malkus DS, Plesha ME, Witt RJ (2001) Concepts and application of finite element analysis, 4th edn. Wiley, United StatesGoogle Scholar
  10. Cowper GR (1966) The shear coefficient in Timoshenko’s beam theory. J Appl Mech 33:335–340CrossRefzbMATHGoogle Scholar
  11. Doyle JF (1989) Wave propagation in structures: an FFT-based spectral analysis methodology. Springer, New YorkCrossRefzbMATHGoogle Scholar
  12. Fink M, Cassereau D, Derode A, Prada C, Roux P, Tanter M, Thomas J-L, Wu F (2000) Time-reversed acoustics. Rep Prog Phys 63(12):1933CrossRefGoogle Scholar
  13. Fink M, Prada C (2001) Acoustic time-reversal mirrors. Inverse Probl 17(1):R1CrossRefzbMATHGoogle Scholar
  14. Fung YC (1965) Foundations of solids mechanics. Prentice-Hall, Englewood Cliffs, New JerseyGoogle Scholar
  15. Givoli D (2014) Time reversal as a computational tool in acoustics and elastodynamics. J Comput Acoust 22(03)Google Scholar
  16. Gopalakrishnan S, Chakraborty A, Mahapatra DR (2008) Spectral finite element method: wave propagation, diagnostics and control in anisotropic and inhomogeneous structures. Springer, LondonzbMATHGoogle Scholar
  17. Graff KF (1975) Wave motion in elastic solids. Dover publications, New YorkzbMATHGoogle Scholar
  18. Guennec YL, Savin E, Clouteau D (2013) A time-reversal process for beam trusses subjected to impulse loads. J Phys Conf Ser 464(012001)Google Scholar
  19. Hartmann F (2013) Green’s functions and finite elements. Springer, BerlinCrossRefzbMATHGoogle Scholar
  20. Kohler MD, Heaton TH, Heckman V (2009) A time-reversed reciprocal method for detecting high-frequency events in civil structures with accelerometer arrays. In: Proceedings of the 5th international workshop on advanced smart materials and smart structures technologyGoogle Scholar
  21. Le Guennec Y, Savin É (2011) A transport model and numerical simulation of the high-frequency dynamics of three-dimensional beam trusses. J Acoust Soc Am 130(6):3706–3722CrossRefGoogle Scholar
  22. Panagiotopoulos CG, Paraskevopoulos EA, Manolis GD (2011) Critical assessment of penalty-type methods for imposition of time-dependent boundary conditions in fem formulations for elastodynamics. In: Computational methods in earthquake engineering. Springer, pp 357–375Google Scholar
  23. Panagiotopoulos CG, Petromichelakis Y, Tsogka C (2015) Time reversal in elastodynamics with application to structural health monitoring. In: Proceedings of the 5th international conference on computational methods in structural dynamics and earthquake engineeringGoogle Scholar
  24. Paraskevopoulos E, Panagiotopoulos C, Manolis G (2010) Imposition of time-dependent boundary conditions in fem formulations for elastodynamics: critical assessment of penalty-type methods. Comput Mech 45:157–166MathSciNetCrossRefzbMATHGoogle Scholar
  25. Prada C, Thomas J-L, Fink M (1995) The iterative time reversal process: analysis of the convergence. J Acoust Soc Am 97(1):62–71CrossRefGoogle Scholar
  26. Przemieniecki J (1968) Theory of matrix structural analysis. Dover publications, Inc., New YorkzbMATHGoogle Scholar
  27. Simo J, Tarnow N (1992) The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics. J Appl Math Phys 43:757–792MathSciNetCrossRefzbMATHGoogle Scholar
  28. Timoshenko SP (1921) On the correction for shear of the differential equation for transverse vibrations of bars of uniform cross-section. Phil Mag 41:744–746CrossRefGoogle Scholar
  29. Timoshenko SP (1922) On the transverse vibrations of bars of uniform cross-section. Phil Mag 43:125–131CrossRefGoogle Scholar
  30. Tsogka C, Petromichelakis Y, Panagiotopoulos CG (2015) Influence of the boundaries in imaging for damage localization in 1D domains. In: Proceedings of the 8th GRACM international congress on computational mechanicsGoogle Scholar
  31. Yavuz ME, Teixeira FL (2009) Ultrawideband microwave sensing and imaging using time-reversal techniques: a review. Remote Sens 1(3):466–495CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • C. G. Panagiotopoulos
    • 1
  • Y. Petromichelakis
    • 1
  • C. Tsogka
    • 1
    • 2
  1. 1.Institute of Applied & Computational MathematicsFoundation for Research and Technology HellasHeraklionGreece
  2. 2.Department of Mathematics & Applied MathematicsUniversity of CreteHeraklionGreece

Personalised recommendations